arXiv subjects

Rudolf Mathar

Publications and source records attributed to Rudolf Mathar.

38 records · Page 3Linked to original sources

arXiv2009

Asymptotic stability and capacity results for a broad family of power adjustment rules: Expanded discussion

In any wireless communication environment in which a transmitter creates interference to the others, a system of non-linear equations arises. Its form (for 2 terminals) is p1=g1(p2;a1) and p2=g2(p1;a2), with p1, p2 power levels; a1, a2 quality-of-service (QoS) targets; and g1, g2 functions akin to "interference functions" in Yates (JSAC, 13(7):1341-1348, 1995). Two fundamental questions are: (1) does the system have a solution?; and if so, (2) what is it?. (Yates, 1995) shows that IF the system has a solution, AND the "interference functions" satisfy some simple properties, a "greedy" power adjustment process will always converge to a solution. We show that, if the power-adjustment functions have similar properties to those of (Yates, 1995), and satisfy a condition of the simple form gi(1,1,...,1)<1, then the system has a unique solution that can be found iteratively. As examples, feasibility conditions for macro-diversity and multiple-connection receptions are given. Informally speaking, we complement (Yates, 1995) by adding the feasibility condition it lacked. Our analysis is based on norm concepts, and the Banach's contraction-mapping principle.

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arXiv2005

Optimal Power Control for Multiuser CDMA Channels

In this paper, we define the power region as the set of power allocations for K users such that everybody meets a minimum signal-to-interference ratio (SIR). The SIR is modeled in a multiuser CDMA system with fixed linear receiver and signature sequences. We show that the power region is convex in linear and logarithmic scale. It furthermore has a componentwise minimal element. Power constraints are included by the intersection with the set of all viable power adjustments. In this framework, we aim at minimizing the total expended power by minimizing a componentwise monotone functional. If the feasible power region is nonempty, the minimum is attained. Otherwise, as a solution to balance conflicting interests, we suggest the projection of the minimum point in the power region onto the set of viable power settings. Finally, with an appropriate utility function, the problem of minimizing the total expended power can be seen as finding the Nash bargaining solution, which sheds light on power assignment from a game theoretic point of view. Convexity and componentwise monotonicity are essential prerequisites for this result.

cs.IT↗